Critical Point of Symmetric Binary Homopolymer Blends

Abstract

Monte Carlo field-theoretic simulations (MC-FTS) are performed on structurally symmetric binary homopolymer blends for invariant polymerization indexes of N ≥ 103. It is shown that the ultraviolet (UV) divergence that plagues MC-FTS at small N can be removed by an appropriate renormalization of the Flory–Huggins interaction parameter, χ, allowing one to extract meaningful results that are independent of the wavevector cutoff. Once the divergence is taken care of, the fluctuation corrections to mean-field theory are found to be exceptionally small. In particular, the disordered-state structure function, S(k), is virtually indistinguishable from the RPA prediction, and there is a slight shift in the critical point, (χN)c, that roughly scales as N–1/2. An implication of the small corrections is that previous experimental determinations of χ based on homopolymer blends should be relatively accurate.